Good self dual codes exist

Abstmt. It is showc that for any block length n which is a multiple of 5, there exists a binary self dual code irr which all weights are divisible by 4, and the minimum weight is asymptotically the same as that given by the Varshamov-Gilbert bound. § 1. Preliminaries Let Fn denote the vector space of all vectors of length II with components from GF(2). The weiglzt of ii vector u = is the number of nonzero uj5 and is denoted by w(u). For vectors u, u in FM we define Clearly w(zl * U) is the number of places in which both Zij and Us are 1. We frequently use the obvious formula w(u + v) = w(u)-I w(9)-2w(u * v) * (1.1)